diff --git a/src/id_map.hh b/src/id_map.hh
index 5a4faa4e..b8593e69 100644
--- a/src/id_map.hh
+++ b/src/id_map.hh
@@ -36,11 +36,16 @@ public:
 
     IdMap(std::initializer_list<Element> val)
         : m_content{val},
-          m_sorted(std::is_sorted(begin(), end(),
-                                  [](const Element& lhs, const Element& rhs)
-                                  { return lhs.hash < rhs.hash; }))
+          m_sorted(std::is_sorted(begin(), end(), cmp_hashes))
     {}
 
+    bool sorted() const { return m_sorted; }
+    void assume_sorted()
+    {
+        kak_assert(std::is_sorted(begin(), end(), cmp_hashes));
+        m_sorted = true;
+    }
+
     void append(const Element& value, bool keep_sorted = false)
     {
         if (keep_sorted and m_sorted)
@@ -61,9 +66,7 @@ public:
     {
         if (keep_sorted and m_sorted)
         {
-            auto it = std::lower_bound(begin(), end(), value.hash,
-                                       [](const Element& e, size_t hash)
-                                       { return e.hash < hash; });
+            auto it = std::lower_bound(begin(), end(), value, cmp_hashes);
             m_content.insert(it, std::move(value));
         }
         else
@@ -143,9 +146,7 @@ public:
 
     void sort()
     {
-        std::sort(begin(), end(),
-                  [](const Element& lhs, const Element& rhs)
-                  { return lhs.hash < rhs.hash; });
+        std::sort(begin(), end(), cmp_hashes);
         m_sorted = true;
     }
 
@@ -164,6 +165,11 @@ public:
     const_iterator end()   const { return m_content.end(); }
 
 private:
+    static bool cmp_hashes(const Element& lhs, const Element& rhs)
+    {
+        return lhs.hash < rhs.hash;
+    }
+
     container_type m_content;
     bool m_sorted;
 };
diff --git a/src/remote.cc b/src/remote.cc
index 0592d0a3..fbf39d0c 100644
--- a/src/remote.cc
+++ b/src/remote.cc
@@ -89,6 +89,7 @@ public:
     void write(const IdMap<Val, domain>& map)
     {
         write<uint32_t>(map.size());
+        write<bool>(map.sorted());
         for (auto& val : map)
         {
             write(val.key);
@@ -220,6 +221,7 @@ template<typename Val, MemoryDomain domain>
 IdMap<Val, domain> read_idmap(int socket)
 {
     uint32_t size = read<uint32_t>(socket);
+    bool sorted = read<bool>(socket);
     IdMap<Val, domain> res;
     res.reserve(size);
     while (size--)
@@ -228,6 +230,8 @@ IdMap<Val, domain> read_idmap(int socket)
         auto val = read<Val>(socket);
         res.append({std::move(key), std::move(val)});
     }
+    if (sorted)
+        res.assume_sorted();
     return res;
 }